How to group this list in to some group whose element have a same number to relate

Question

I have this list

list={{0,7},{16,0},{16,2},{12,5},{11,1},{1,20},{3,20}};

This is my current method to realize it.

ConnectedComponents@RelationGraph[IntersectingQ, list]

{{{16, 2}, {16, 0}, {0, 7}}, {{11, 1}, {1, 20}, {3, 20}}, {{12, 5}}}

But are there non-graph and concise solution can implement this target?

Answer 1

list = {{0, 7}, {16, 0}, {16, 2}, {12, 5}, {11, 1}, {1, 20}, {3, 20}};

EdgeList /@ ConnectedGraphComponents@
   Graph[UndirectedEdge @@@ list] /.
 UndirectedEdge -> List

(*  {{{16, 2}, {16, 0}, {0, 7}}, {{11, 1}, {1, 20}, {3, 20}}, {{12, 5}}}  *)

Very slightly shorter,

Apply[List,
 EdgeList /@ ConnectedGraphComponents@
   Graph[UndirectedEdge @@@ list], {2}]

(*  {{{16, 2}, {16, 0}, {0, 7}}, {{11, 1}, {1, 20}, {3, 20}}, {{12, 5}}}  *)

% === %%

(*  True  *)

Without using any Graph functions you can get equivalent (graphs are undirected) but differently ordered results.

list = {{0, 7}, {16, 0}, {16, 2}, {12, 5}, {11, 1}, {1, 20}, {3, 20}};

Partition[#, 2, 
   1] & /@ (list //. {{s___, {x1_, i1___, y1_}, m___, {y1_, i2___, y2_}, 
      e___} :>
     {s, {x1, i1, y1, i2, y2}, m, e},
    {s___, {x1_, i1___, y1_}, m___, {x2_, i2___, x1_}, e___} :>
     {s, {x2, i2, x1, i1, y1}, m, e},
    {s___, {x1_, i1___, y1_}, m___, {x1_, i2___, y2_}, e___} :>
     {s, {y2, Sequence@Reverse@{i2}, x1, i1, y1}, m, e},
    {s___, {x1_, i1___, y1_}, m___, {x2_, i2___, y1_}, e___} :>
     {s, {x1, i1, y1, Sequence@Reverse@{i2}, x2}, m, e}, {} :> Nothing})

(*  {{{2, 16}, {16, 0}, {0, 7}}, {{12, 5}}, {{11, 1}, {1, 20}, {20, 3}}}  *)

Answer 2

The code is ugly,I don't like the If here especially,anyway it works.:)

list = {{0, 7}, {16, 0}, {16, 2}, {12, 5}, {11, 1}, {1, 20}, {3, 20}};
FixedPoint[
 Function[l, temp = Gather[l, ContainsAny[Flatten@#, Flatten[#2]] &]; 
  If[Depth[temp] > 4, Catenate/@temp, temp]], list]

{{{0, 7}, {16, 0}, {16, 2}}, {{12, 5}}, {{11, 1}, {1, 20}, {3, 20}}}